Multiple choice

Marks obtained by 60 students of a class are shown as Marks 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Number of students 8 7 $f_1$ 15 5 $f_2$ 7 the mean marks are 64, then $f_1$ : $f_2$ is

  1. $7 : 4$
  2. $4 : 5$
  3. $5 : 4$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total students = 8 + 7 + f1 + 15 + 5 + f2 + 7 = 42 + f1 + f2 = 60. Thus, f1 + f2 = 18. Using the mean formula (sum of f*x / sum of f) = 64 with midpoints: (35*8 + 45*7 + 55*f1 + 65*15 + 75*5 + 85*f2 + 95*7) / 60 = 64. Solving this system gives f1 = 10 and f2 = 8. The ratio f1 : f2 = 10 : 8 = 5 : 4.

AI explanation

Using the step-deviation method for the mean, let the assumed mean A be 65 and the class size h be 10; the mean is A + (sum of f times u divided by total students) times h. We know the total frequency is 60, so 8 + 7 + f1 + 15 + 5 + f2 + 7 = 60, giving f1 + f2 = 18. Substituting the sum and mean into the formula gives the equation 64 = 65 + ((3f2 - 4f1 - 16) / 60) times 10, which simplifies to 4f1 - 3f2 = 10; solving this with f1 + f2 = 18 results in f1 = 10 and f2 = 8, making their ratio 5 : 4.

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